Abstract:

A system and method for predicting fatigue life in metal alloys for very
high cycle fatigue applications. The system and method are especially
useful for cast metal alloys, such as cast aluminum alloys, where a
fatigue endurance limit is either non-existent or hard to discern.
Fatigue properties, such as fatigue strength in the very high cycle
fatigue region, are based on a modified random fatigue limit model, where
the very high cycle fatigue strength and infinite life fatigue strength
are refined to take into consideration the sizes of the discontinuities
and microstructure constituents since the fatigue life scatter depends
upon the presence of discontinuities and microstructure constituents. The
sizes of the discontinuities and microstructure constituents that can
initiate fatigue cracks can be determined with extreme value statistics,
then input to the modified random fatigue limit model.

Claims:

1. A method of predicting very high cycle fatigue strength for a metal
alloy, said method comprising:selecting an alloy where at least one
fatigue crack initiation site is presumed or determined to be present
therein and where said alloy is generally not possessive of an
identifiable endurance limit;inputting a size of discontinuity or
microstructure constituent representative of said at least one fatigue
crack initiation site;inputting a finite life fatigue strength that
corresponds to said alloy; andcalculating an infinite life fatigue
strength and said very high cycle fatigue strength using a modified
random fatigue limit model.

2. The method of claim 1, wherein said modified random fatigue limit model
comprises using the
equationln(ai.sup.αNf)=C0+C1
ln(σa-.sigma.L)where ai is said size of
discontinuity or microstructure constituent, Nf is fatigue life,
C0 and C1 are constants, α is a constant in the range of
between one and ten, σa is an applied stress, and
σL is a measure of said infinite life fatigue strength.

3. The method of claim 2, wherein said applied stress comprises said very
high cycle fatigue strength in situations where said fatigue life is at
least 10.sup.8 cycles.

4. The method of claim 2, wherein a distribution of said infinite life
fatigue strength substantially follows the equation P = 1 - exp (
- σ L σ 0 ) β ##EQU00013## where P is the
probability of failure at an infinite number of cycles, and σ0
and β are parameters for a distribution of said infinite life
fatigue strength.

5. The method of claim 1, wherein said finite life fatigue strength
comprises the fatigue strength at a fatigue life of up to ten million
cycles.

9. The method of claim 1, wherein at least one fatigue crack initiation
site is determined by at least one of direct measurement and analytical
prediction.

10. The method of claim 9, wherein said direct measurement comprises at
least one of X-ray computed tomography, single and serial sectioning
metallography and fractography.

11. The method of claim 2, wherein said size of said discontinuity or
microstructure constituent follows a generalized extreme value
distribution according to the equation: P = exp ( - ( 1 + c ( a
i - μ a 0 ) ) - 1 c ) ##EQU00014## where c, a0 and
μ are generalized extreme value parameters used to represent at least
one of a shape and a scale of a probabilistic distribution function of
ai.

12. The method of claim 11, wherein said extreme value distribution is
used in conjunction with at least one of 2D metallographic techniques,
fractographic techniques, X-ray computed tomography and computational
simulation and modeling to estimate values representing a population of
said size of discontinuity or microstructure constituent.

13. An article of manufacture comprising a computer-usable medium having
computer-readable program code embodied therein for calculating at least
one of very high cycle fatigue strength and infinite life fatigue
strength in a metal casting where an endurance limit associated with said
metal casting is either not existent or not readily identifiable, said
computer-readable program code in said article of manufacture
comprising:computer-readable program code portion for causing a computer
to determine an infinite life fatigue strength of said metal casting
where at least one fatigue crack initiation site is presumed or
determined to be present therein;computer-readable program code portion
for receiving a discontinuity size representative associated with said at
least one fatigue crack initiation site;computer-readable program code
portion for calculating said fatigue strength based on a modified random
fatigue limit model; andcomputer-readable program code portion configured
to output results calculated by said modified random fatigue life model
to at least one of a machine-readable format and a human-readable format.

14. The article of manufacture of claim 13, wherein said computer-readable
program code portion for calculating at least one of said very high cycle
fatigue strength and infinite life fatigue strength comprises using the
equationln(ai.sup.αNf)=C0+C1
ln(σa-.sigma.L)to effect said modified random fatigue
limit model, where ai is said discontinuity and microstructure
constituent size, Nf is fatigue life, C0 and C1 are
empirical constants, α is a constant in the range of between one
and ten, σa is an applied stress and σL is a
measure of said infinite life fatigue strength.

15. The article of manufacture of claim 14, wherein said computer-readable
program code portion for calculating said fatigue strength comprises
using a generalized extreme value distribution in conjunction with a
modified random fatigue limit model.

16. An apparatus for predicting fatigue life in metal alloys where an
endurance limit associated with the alloy is either not existent or not
readily identifiable, said apparatus comprising:a device configured to
acquire at least one of measured or predicted fatigue crack initiation
site information; anda computing member configured to accept fatigue
property data gathered from said device and further configured to
calculate at least one of a very high cycle fatigue strength and an
infinite fatigue life strength of the alloy in accordance to instructions
provided by a computer-readable program, said program comprising:a code
portion for causing said computing member to determine said at least one
of a very high cycle fatigue strength and an infinite life fatigue
strength of the alloy where at least one fatigue crack initiation site is
presumed or determined to be present therein;a code portion for receiving
at least one of a discontinuity size and a microstructure constituent
size associated with said at least one fatigue crack initiation site;a
code portion for calculating said at least one of a very high cycle
fatigue strength and an infinite fatigue life strength based on a
modified random fatigue limit model; anda code portion configured to
output results calculated by said MRFL model to at least one of a
machine-readable format and a human-readable format.

17. The apparatus of claim 16, wherein said program further comprises at
least one extreme value statistical algorithm to estimate an upper bound
initiation site size expected to occur in the alloy.

18. The apparatus of claim 16, wherein said computer-readable program code
portion for calculating said at least one of a very high cycle fatigue
strength and an infinite life fatigue strength comprises using the
equationln(ai.sup.αNf)=C0+C1
ln(σa-.sigma.L)to effect said modified random fatigue
limit model, where ai is said discontinuity and microstructure
constituent size, Nf is fatigue life, C0 and C1 are
empirical constants, α is a constant in the range of between one
and ten, σa is an applied stress and σL is a
measure of said infinite life fatigue strength.

Description:

BACKGROUND OF THE INVENTION

[0001]The present invention relates generally to methods and systems of
predicting fatigue life in metal alloys, and more particularly to using
probabilistic models and high cycle fatigue behavior for predicting very
high cycle fatigue life in aluminum and related metals. Even more
particularly, the invention relates to predicting fatigue life in cast
aluminum alloy objects at very high cycle fatigue levels.

[0002]The increased demand for improving fuel efficiency in automotive
design includes an emphasis on reducing component mass through the use of
lightweight materials in the construction of vehicle component parts,
including in the powertrain and related componentry. Cast lightweight
non-ferrous alloys in general, and aluminum alloys in particular are
increasingly being used in, but are not limited to engine blocks,
cylinder heads, pistons, intake manifolds, brackets, housings, wheels,
chassis, and suspension systems. In addition to making such components
lighter, the use of casting and related scalable processes helps to keep
production costs low.

[0003]As many of the applications of cast aluminum and other lightweight
metal alloys in vehicle components involve very high cycle (generally,
more than 108 cycles, and often associated with between 109 and
1011 cycles) loading, the fatigue properties, particularly the very
high cycle fatigue (VHCF) properties, of the alloys are critical design
criteria for these structural applications. Fatigue properties of cast
aluminum components are strongly dependent upon discontinuities (that
often initiate fatigue cracks), such as voids and related porosity, or
oxide films or the like, that are produced during casting. Moreover, the
probability of having a casting discontinuity in a given portion of the
casting depends on many factors, including melt quality, alloy
composition, casting geometry and solidification conditions. Given these
factors, as well as inherent nonhomogeneities of the material, it can be
appreciated that the nature of fatigue is probabilistic, where prediction
of expected behavior over a range of loads is more meaningful that trying
to establish a precise, reproducible fatigue value.

[0004]Despite this, there are factors that provide good indicators of
fatigue behavior. For example, cracks readily initiate from large
discontinuities that are located near or at the free surface of
components and are subjected to cyclic loading, and the size of such
cracking is important to determining the fatigue life of a component. As
a general proposition, the resulting fatigue strength for a given number
of cycles to failure, or life for a given load, is inversely proportional
to the size of the discontinuities that initiate fatigue cracks.

[0005]One particular form of fatigue, known as high cycle fatigue (HCF),
is concerned with the repeated application of cyclic stresses for a large
number of times. The most commonly-cited value for such large number of
times is about ten million (107). The suitability of many structural
materials (for example, ferrous-based and non-ferrous based alloys) for
use in components and applications where HCF is a concern is often
measured by familiar means, such as from the data in well-known S-N
curves, examples of which are shown in FIGS. 1 and 2A where the number of
completely reversed stress cycles that the material will survive
decreases with an increase in stress level. Referring with particularity
to FIG. 1, the fatigue strengths and corresponding S-N curves for many
materials (for example, ferrous-based alloys) have a tendency to flatten
out above a certain number of cycles at a stress known as the endurance
limit. In general, the endurance limit is the maximum stress that may be
applied to the material through an indefinite number of such completely
reversed cycles without failure.

[0006]Unfortunately, aluminum-based alloys (also shown in FIG. 1) do not
show a clearly-defined endurance limit, instead exhibiting successively
lower levels of allowable cyclic stresses, for fatigue lives in the
millions to trillions of cycles. Such alloys are considered to be
generally not possessive of an endurance limit, or if possessive of one,
are such that the endurance limit is not generally discernable or readily
quantified. In either event, it is difficult to determine an appropriate
design strength (under cyclic loading) and related material properties of
cast aluminum alloys beyond either the HCF limit or those associated with
very high cycle fatigue (VHCF, typically from about 108 to 1011
or more cycles). Since long-term properties of components made from such
alloys are critical to their success and are considered to be important
design criteria for these components in structural applications,
additional methods of determining strength and related properties for
cast aluminum alloys in a manner generally similar to that used to
predict the fatigue behavior of ferrous-based alloys are desired.

[0007]The well-known Wohler test (the results of which can be used to
produce the aforementioned S-N curve) and staircase fatigue test (the
results of which are depicted in FIG. 2B) are commonly used to
characterize the fatigue properties of materials for conventional HCF
(e.g. 107) life cycles. The statistical analysis of the results of
these two fatigue tests is usually based on the assumption that the
fatigue strength is normally distributed. As a result, the results
generally agree for estimations of median fatigue strength, but show
significant differences (up to, for example, a factor of two) in their
standard deviation. One of the disadvantages of the staircase fatigue
test is that the fatigue strength tested and calculated is restricted to
a fixed number of cycles (for example, around 104 cycles for low
cycle fatigue (LCF), and 107 cycles for HCF). In comparison with the
staircase fatigue test, the S-N curve from the Wohler test can offer
fatigue strengths at different numbers of cycles to fracture. Whether
using Wohler or staircase testing, conventional servo-hydraulic fatigue
testing systems operate at nominal frequencies of no more than a hundred
or so cycles per second, making it time-wise impractical to generate S-N
or related curves for VHCF applications, where 108 through 1011
(or more) cycles are experienced. Accordingly, it would be desirable to
be able to estimate strength and related material properties of cast
aluminum alloys beyond the HCF limit, including the VHCF range.

BRIEF SUMMARY OF THE INVENTION

[0008]These desires are met by the present invention, wherein improved
methods and systems that employ probabilistic approaches to estimate VHCF
properties of cast aluminum and other non-ferrous alloys are disclosed.
These approaches can be based on S-N and staircase fatigue data for
conventional HCF (i.e., up to about 107 cycles) and discontinuity
and microstructure constituent populations in the materials of interest.

[0009]In accordance with a first aspect of the present invention, a method
is used for predicting VHCF strength for a metal alloy. The method
includes selecting an alloy where at least one fatigue crack initiation
site is presumed or determined to be present and where the alloy is
generally not possessive of an identifiable endurance limit. The method
further includes inputting a discontinuity or microstructure constituent
size representative of the fatigue crack initiation site. From that, the
method can be used to calculate VHCF strength and an infinite life
fatigue strength based on a modified random fatigue limit (MRFL) model.

[0010]Optionally, the MRFL model includes using Eqn. 2, discussed in more
detail below. In a more particular version, the size of the discontinuity
or microstructure constituent that initiates fatigue cracking is
introduced in the model. This extends the MRFL model to be applicable to
the same material but with different discontinuity and microstructure
constituent populations. In a particular form, the metal alloy comprises
a cast aluminum alloy. It will be appreciated by those skilled in the art
that other non-ferrous metal alloys can be used, including wrought and
related non-cast alloys, as well as those of other non-ferrous metals,
such as magnesium. In another option, one or more fatigue crack
initiation sites are determined by at least one of direct measurement and
analytical prediction, where the direct measurement is selected from one
of X-ray computed tomography, single and serial sectioning metallography,
fractography or related methods. In another option, the infinite life
fatigue limit follows a distribution according to Eqn. 3 that is
discussed in more detail below. In an even more particular option, the
size of the discontinuity or microstructure constituent follows a
generalized extreme value distribution according to Eqn. 4 as discussed
in more detail below. The present inventors have additionally discovered
that fatigue performance of a given volume element in a cast aluminum
component is controlled by extremes in the discontinuity and
microstructure constituent size, and as such may benefit from the use of
Extreme Value Statistics (EVS) in making predictions about the fatigue
life of aluminum-based alloys. In situations where the fatigue life of
the alloy extends beyond conventional HCF values and into the VHCF regime
(for example, at least 108 cycles), the applied stress is also used
as a VHCF strength from Eqn. 2, discussed in more detail below.

[0011]In accordance with a second aspect of the present invention, an
article of manufacture useable to predict fatigue life in metal castings
is disclosed. The article of manufacture comprises a computer-usable
medium having computer-executable instructions adapted to such fatigue
life predictions. The computer-executable instructions comprise equations
used to determine fatigue life properties based upon various constants,
input conditions and nature of a fatigue-inducing condition. The article
is particularly well-suited for predicting VHCF fatigue life, where an
endurance limit associated with a metal casting is either not existent or
not readily identifiable. In the present context, an endurance limit is
considered non-existent when there is no substantially fixed maximum
stress level below which a material can endure a substantially infinite
number of stress cycles without failing. Likewise, the endurance limit is
not readily identifiable if after a large number of stress cycles, an
appropriate measure (for example, an S-N curve) does not reveal a
substantially constant maximum stress level.

[0012]Optionally, the computer-readable program code portion for
calculating the VHCF strength comprises using a generalized extreme value
distribution in conjunction with the equations associated with the MRFL
model.

[0013]In accordance with a third aspect of the present invention, an
apparatus for predicting VHCF life in a metal alloy is disclosed. The
apparatus includes a computing device such as discussed in the previous
aspect, and may additionally include sample sensing equipment examples of
which may include fatigue measuring components, as well as components
capable of inducing and measuring tension, compression, impact and
hardness properties of various structural materials under precisely
controlled conditions. Such equipment (many examples of which are
commercially available) may be operatively coupled to the computing
device such that sensed data taken from the equipment can be operated
upon by computer-readable software to, among other things, calculate
fatigue properties of the sampled alloy. In other forms, the sample
sensing equipment may be a sensor configured to identify discontinuities,
cracks and related flaws that may serve as fatigue crack initiation
sites. Such equipment may operate using machine vision or any other
method known to those skilled in the art to detect such defects. The
computing member includes program code to effect calculations of infinite
life fatigue strengths based on one or more of the equations discussed
below.

[0014]Optionally, the program further comprises at least one extreme value
statistical algorithm to estimate an upper bound initiation site size
expected to occur in the alloy. The code portion for calculating the
infinite life fatigue strength comprises using the MRFL equations.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[0015]The following detailed description of the present invention can be
best understood when read in conjunction with the following figures:

[0016]FIG. 1 shows a representative S-N plot for both a ferrous alloy and
an aluminum alloy;

[0017]FIG. 2A shows a plot of data for an S-N test on a cast A356 aluminum
alloy;

[0018]FIG. 2B shows a plot of data and procedure for a staircase fatigue
test on a cast A356 aluminum alloy;

[0019]FIG. 3 shows a generalized extreme value distribution of porosity
size characterized by the pore area for a cast A356 sample;

[0020]FIG. 4 shows an estimation of VHCF for a lost foam casting of A356
aluminum alloy using a MRFL model according to an embodiment of the
present invention, as well as a comparison to the S-N data of FIG. 2A;
and

[0021]FIG. 5 shows an article of manufacture incorporating an algorithm
employing one or more of the equations used in the MRFL model.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0022]Referring with particularity to FIG. 4, the MRFL model is used to
predict the fatigue strengths of cast aluminum components for very long
lives (108 cycles and higher). The MRFL model proposed in this
invention is based on an earlier random fatigue limit model where the
finite fatigue lives can be calculated as follows:

ln(Nf)=B0+B1 ln(Sa-SL)+ξ (1)

where ξ represents the scatter in fatigue lives, B1 and B1
are constants, and SL is the infinite fatigue limit of the specimen.

[0023]For a given stress state, the scatter of the fatigue lives of cast
aluminum components is believed to be mainly related to the presence of
discontinuities and microstructure constituents in general, and in
particular to their sizes. As such, the present inventors felt that the
random fatigue limit model of Eqn. 1 should be modified to incorporate
the discontinuity and microstructure constituent sizes, thereby improving
model accuracy and applicability to cast aluminum alloys. Eqn. 2 is a
representation of how the random fatigue limit model of Eqn. 1 should be
modified:

ln(ai.sup.αNf)=C0+C1
ln(σa-σL) (2)

where C0 and C1 are empirical constants, α is a constant
(in the range of 1-10), σa is the applied stress, and ai
is the size of the discontinuity or microstructure constituent at which
the fatigue crack nucleates. In this invention, the ai is assumed to
be equal to the defect size in the case of a volume containing a defect,
to the second phase particle size, or to the size of the mean free path
in the aluminum matrix. As with the value SL in Eqn. 1,
σL is the infinite life fatigue limit of the specimen. The
present inventors believe that the infinite life fatigue limit
σL will follow a Weibull distribution given by Eqn. (3):

P = 1 - exp ( - σ L σ 0 ) β ( 3
) ##EQU00001##

where P is the probability of failure at an infinite number of cycles, and
σ0 and β are the Weibull parameters for the infinite life
fatigue limit distribution.

[0024]In comparison with the earlier random fatigue limit model of Eqn. 1,
the MRFL model of Eqn. 2 is not only more physically sound, but also more
accurate in life prediction. For example, while the model constants in
the earlier random fatigue limit model of Eqn. 1 have to be refitted when
the discontinuity and material constituents change, even for the same
alloy and material, no such change is needed in the MRFL model.
Specifically, the model constants do not need to change for different
populations of discontinuity and microstructure constituents in the same
material and alloy. This is advantageous in that the discontinuity
population can vary with normal process variation, such as seasonal
humidity changes that affect the amount of hydrogen dissolved in the
liquid aluminum, which in turn impacts the size of pores in the
solidified component.

[0025]Referring to methods to estimate the parameters of a statistical
distribution from a set of data, the Maximum Likelihood (ML) method is
used by the inventors because of its good statistical properties. The
main advantages of the ML method are the ability to correctly treat
censored data and the fact that any distribution can be used (as long as
the likelihood equations are known). The likelihood equations are
functions of the experimental data and the unknown parameters that define
the distribution.

[0026]In a staircase fatigue test, for instance, if a specimen tested at
stress amplitude σa does not fail after, say, 107 cycles,
it can be assumed that the fatigue strength for this specimen is
certainly higher than σa. If the specimen fails, however, then
the fatigue strength should be lower than σa. If
F(σai{p}) is the cumulative density function for the
distribution chosen to represent the fatigue strength variability in the
staircase test, then the likelihood function for the staircase tests is
defined as

where n corresponds to the number of failed specimens and m is the number
of runouts, {p} are the parameters that define the fatigue strength
distribution for the specified number of cycles. In S-N tests, the
likelihood of fatigue life for a given stress amplitude σa can
be defined as follows:

where n corresponds to the number of failed specimens and m is the number
of runouts, f(NFi, {p}) is the probability density function,
F(NRj, {p}) is the cumulative density function, and {p} are the
parameters that define the fatigue life distribution for a given applied
stress.

[0027]Referring next to probability of the size of discontinuity and
microstructure constituents (ai in Eqn. 2) in a cast aluminum
object, a generalized extreme value distribution is used. It is well
known that fatigue cracks initiate at the largest "weak link" feature in
the volume of material exposed to cyclic stress. Therefore when choosing
the scale of fatigue crack initiator candidates, the upper bound of the
available population should be considered. This is accomplished by
estimating the upper bound using various EVS methods, or by directly
measuring crack initiation sites which are themselves representative of
the upper bound of the available population in a given volume. A
representation of how the size of discontinuity or microstructure
constituents follows a generalized extreme value distribution (GEVD) when
the measurements were made directly from the crack initiation sites is as
follows:

P = exp ( - ( 1 + c ( a i - μ a 0 ) ) - 1 c
) ( 6 ) ##EQU00004##

where c, a0 and μ are the GEVD parameters that represent the shape
and scale of the probabilistic distribution function of ai. The
determination of three parameters, c, a0 and μ is made by using
the ML method. FIG. 3 shows an example of pore size (for example
characterized as ai= {square root over (pore area)}) using a GEVD
for a cast A356 sample.

[0028]Metallographic techniques are widely utilized in practice to
characterize casting flaws and microstructures in two dimensions (2D).
With the conventional 2D metallographic data, the size distributions of
casting flaws, inclusions and other microstructure features can be well
described by EVS with a cumulative distribution function such as:

F ( x ) = exp ( - exp ( - x - λ δ ) )
( 7 ) ##EQU00005##

where x is the characteristic parameter of flaws or microstructural
features, and λ and δ are referred to as the EVS location and
the scale parameters (also referred to as distribution parameters),
respectively. It will be appreciated by those skilled in the art that
while Eqn. 7 is used in the present disclosure to produce a cumulative
distribution function, it is merely exemplary of such functions, and
other similar distribution functions can be used to best fit the
experimental data.

[0029]Considering a population of flaws or microstructure features as an
example, an estimate of the distribution parameters λ and δ
can be made by different methods, where the most commonly used and
convenient method is ordering/ranking statistics together with a linear
regression. The characteristic flaw or microstructural feature parameters
are ordered from the smallest to the largest with each assigned a
probability based on its ranking j as follows:

F = j - 0.5 n ( 8 ) ##EQU00006##

where n is the total number of data points. Eqn. 7 can be rearranged to a
linear equation by twice taking its natural logarithm and transforming
the parameters F(x) to ln(-ln F(x)) and the parameter x as follows:

- ln ( - ln ( F ( x ) ) ) = 1 δ x -
λ δ . ( 9 ) ##EQU00007##

[0030]The EVS parameters λ and δ can then be calculated from
ML, moment or least squares methods. When the sample size is small (for
example, approximately 30 flaws or microstructure features), the ML
method gives the most efficient estimates. For a large number of samples
(for example, where n from Eqn. 8 is greater than about 50), the ML,
moment, and least square methods give similar precision.

[0031]The characteristic flaw or microstructure feature parameters
predicted by EVS depend on the volume of material for which the
prediction is sought. The volume effect is accounted for by the return
period T, where two such periods, T and Tb, are considered. T
accounts for the volume sampled compared to the volume of one part. The T
return period of the maximal flaw or microstructure features in a given
casting is usually determined by:

T = V V 0 ( 10 ) ##EQU00008##

where V is the volume of a casting and V0 is the volume of the
specimen for flaw or microstructure features measurement.

[0032]Next, the volume effect is extrapolated to represent the population.
The population is represented by a batch of N castings. The return period
of the extreme flaw or microstructure features occurring once in a batch
of N castings is:

Tb=T*N (11)

[0033]Once the volume effects are accounted for, the characteristic flaw
or microstructure feature parameters can be estimated using:

x ( T b ) = λ - δ ln [ - ln ( 1 - 1
T b ) ] ( 12 ) ##EQU00009##

and three sigma (i.e., minimum theoretical 99.94%) estimates on the
maximal flaw or microstructure feature characteristic parameter can be
made. The standard deviation is estimated by the Cramer-Rao lower bound:

[0035]EVS can estimate the maximum 3D characteristic dimensions, which are
otherwise difficult and costly to obtain, from readily available 2D
measurements. It will be appreciated that if actual 3D dimensions for any
given portion of a casting sample are determined, EVS may not be needed.

[0036]Referring again to FIG. 4, the predictions of the MRFL model
compared with the experimental measurements in S-N curves show that
incorporating discontinuity (such as porosity) size, calculated from Eqn.
6, in the MRFL model provides good fatigue property predictions,
especially in the VHCF regime. Specifically, the predictions of the MRFL
model compared with the experimental measurements in S-N curves show that
incorporating second phase particle size estimated using Eqn. 6 in the
MRFL model provides good fatigue property predictions.

[0037]Referring next to FIG. 5, the MRFL model discussed above may be
embodied in an algorithm that can be run on a computation device 200.
Computation device 200 (shown in the form of a desktop computer, but
understood by those skilled in the art as also capable of being a
mainframe, laptop, hand-held, cellular or other related
microprocessor-controlled device) includes a central processing unit 210,
input 220, output 230 and memory 240, the latter of which may include
random access memory (RAM) 240A and read-only memory (ROM) 240B, where
the former generally refers to volatile, changeable memory and the latter
to more permanent, non-alterable memory. With recent developments, such
distinctions between RAM 240A and ROM 240B are becoming increasingly
evanescent, and while either ROM 240B or RAM 240A could be used as a
computer-readable medium upon which program code representative of some
or all of the aforementioned fatigue life prediction equations can be
run, it will be understood by those skilled in the art that when such
program code is loaded into the computation device 200 for subsequent
reading and operation upon by the central processing unit 210, it will
typically reside in RAM 240A. Thus, in one preferable form, the algorithm
can be configured as computer-readable software such that when loaded
into memory 240, it causes a computer to calculate fatigue life based on
a user's input. The computer-readable medium containing the algorithm can
additionally be introduced into computation device 200 through other
portable means, such as compact disks, digital video disks, flash memory,
floppy disks or the like. Regardless of the form, upon loading, the
computer-readable medium includes the computer-executable instructions
adapted to effect the decision-making process of the MRFL model. As will
be appreciated by those skilled in the art, the computation device 200
may optionally include peripheral equipment. Moreover, the computation
device 200 may form the basis for a system that can be used to predict
fatigue life in aluminum castings. The system may additionally include
measuring, testing and sampling equipment (not shown) such that fatigue
data taken directly from a sample casting may be loaded into memory 240
or elsewhere for subsequent comparison to predicted data or the like.

[0038]While certain representative embodiments and details have been shown
for purposes of illustrating the invention, it will be apparent to those
skilled in the art that various changes may be made without departing
from the scope of the invention, which is defined in the appended claims.